Rosa's TurbineBenchmark

Average Error: 12.8 → 1.2

Time: 49.8s

Precision: 64

Math

\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]

↓

\[\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1 - v}}} \cdot \left(\left(\left(\left(w \cdot \left(r \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right)\right) \cdot \left(w \cdot \left(r \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{0.125}}}\right)\]

C

double f(double v, double w, double r) {
        double r2368448 = 3.0;
        double r2368449 = 2.0;
        double r2368450 = r;
        double r2368451 = r2368450 * r2368450;
        double r2368452 = r2368449 / r2368451;
        double r2368453 = r2368448 + r2368452;
        double r2368454 = 0.125;
        double r2368455 = v;
        double r2368456 = r2368449 * r2368455;
        double r2368457 = r2368448 - r2368456;
        double r2368458 = r2368454 * r2368457;
        double r2368459 = w;
        double r2368460 = r2368459 * r2368459;
        double r2368461 = r2368460 * r2368450;
        double r2368462 = r2368461 * r2368450;
        double r2368463 = r2368458 * r2368462;
        double r2368464 = 1.0;
        double r2368465 = r2368464 - r2368455;
        double r2368466 = r2368463 / r2368465;
        double r2368467 = r2368453 - r2368466;
        double r2368468 = 4.5;
        double r2368469 = r2368467 - r2368468;
        return r2368469;
}

↓

double f(double v, double w, double r) {
        double r2368470 = 2.0;
        double r2368471 = r;
        double r2368472 = r2368471 * r2368471;
        double r2368473 = r2368470 / r2368472;
        double r2368474 = 3.0;
        double r2368475 = 4.5;
        double r2368476 = r2368474 - r2368475;
        double r2368477 = r2368473 + r2368476;
        double r2368478 = 0.125;
        double r2368479 = sqrt(r2368478);
        double r2368480 = cbrt(r2368479);
        double r2368481 = sqrt(r2368480);
        double r2368482 = 1.0;
        double r2368483 = v;
        double r2368484 = r2368482 - r2368483;
        double r2368485 = cbrt(r2368484);
        double r2368486 = cbrt(r2368485);
        double r2368487 = r2368481 / r2368486;
        double r2368488 = w;
        double r2368489 = cbrt(r2368478);
        double r2368490 = r2368489 / r2368485;
        double r2368491 = r2368471 * r2368490;
        double r2368492 = r2368488 * r2368491;
        double r2368493 = r2368492 * r2368492;
        double r2368494 = r2368470 * r2368483;
        double r2368495 = r2368474 - r2368494;
        double r2368496 = r2368486 * r2368486;
        double r2368497 = r2368480 / r2368496;
        double r2368498 = r2368495 * r2368497;
        double r2368499 = r2368493 * r2368498;
        double r2368500 = r2368499 * r2368481;
        double r2368501 = r2368487 * r2368500;
        double r2368502 = r2368477 - r2368501;
        return r2368502;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Derivation

1. Initial program 12.8

   \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]

2. Simplified 7.0

   \[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{0.125}{1 - v}}\]
3. Using strategy rm

4. Applied add-cube-cbrt 7.0

   \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{0.125}{\color{blue}{\left(\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}\right) \cdot \sqrt[3]{1 - v}}}\]

5. Applied add-cube-cbrt 7.2

   \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}\right) \cdot \sqrt[3]{0.125}}}{\left(\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}\right) \cdot \sqrt[3]{1 - v}}\]

6. Applied times-frac 7.2

   \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right)}\]

7. Applied associate-*r* 7.3

   \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\sqrt[3]{0.125} \cdot \sqrt[3]{0.125}}{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}\right) \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}}\]

8. Simplified 2.7

   \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right)} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\]
9. Using strategy rm

10. Applied add-cube-cbrt 2.7

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\sqrt[3]{0.125}}{\color{blue}{\left(\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}\right) \cdot \sqrt[3]{\sqrt[3]{1 - v}}}}\]

11. Applied add-sqr-sqrt 2.7

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\sqrt[3]{\color{blue}{\sqrt{0.125} \cdot \sqrt{0.125}}}}{\left(\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}\right) \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\]

12. Applied cbrt-prod 2.5

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\color{blue}{\sqrt[3]{\sqrt{0.125}} \cdot \sqrt[3]{\sqrt{0.125}}}}{\left(\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}\right) \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\]

13. Applied times-frac 2.5

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}} \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)}\]

14. Applied associate-*r* 2.5

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right)\right) \cdot \left(3 - 2 \cdot v\right)\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}\]

15. Simplified 1.3

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right)} \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\]
16. Using strategy rm

17. Applied *-un-lft-identity 1.3

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{\color{blue}{1 \cdot \left(1 - v\right)}}}}\]

18. Applied cbrt-prod 1.3

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{1 - v}}}}\]

19. Applied cbrt-prod 1.3

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\color{blue}{\sqrt[3]{\sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}}\]

20. Applied add-sqr-sqrt 1.2

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \frac{\color{blue}{\sqrt{\sqrt[3]{\sqrt{0.125}}} \cdot \sqrt{\sqrt[3]{\sqrt{0.125}}}}}{\sqrt[3]{\sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\]

21. Applied times-frac 1.2

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \color{blue}{\left(\frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1}}} \cdot \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)}\]

22. Applied associate-*r* 1.2

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right) \cdot \left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot \left(r \cdot w\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1}}}\right) \cdot \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}}\]

23. Simplified 1.2

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \color{blue}{\left(\left(\left(\left(3 - v \cdot 2\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\right) \cdot \left(\left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot r\right) \cdot w\right) \cdot \left(\left(\frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}} \cdot r\right) \cdot w\right)\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{0.125}}}\right)} \cdot \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1 - v}}}\]

24. Final simplification 1.2

    \[\leadsto \left(\frac{2}{r \cdot r} + \left(3 - 4.5\right)\right) - \frac{\sqrt{\sqrt[3]{\sqrt{0.125}}}}{\sqrt[3]{\sqrt[3]{1 - v}}} \cdot \left(\left(\left(\left(w \cdot \left(r \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right)\right) \cdot \left(w \cdot \left(r \cdot \frac{\sqrt[3]{0.125}}{\sqrt[3]{1 - v}}\right)\right)\right) \cdot \left(\left(3 - 2 \cdot v\right) \cdot \frac{\sqrt[3]{\sqrt{0.125}}}{\sqrt[3]{\sqrt[3]{1 - v}} \cdot \sqrt[3]{\sqrt[3]{1 - v}}}\right)\right) \cdot \sqrt{\sqrt[3]{\sqrt{0.125}}}\right)\]

Reproduce

herbie shell --seed 2019192 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3.0 (/ 2.0 (* r r))) (/ (* (* 0.125 (- 3.0 (* 2.0 v))) (* (* (* w w) r) r)) (- 1.0 v))) 4.5))